On the girth of digraphs

  title={On the girth of digraphs},
  author={Jian Shen},
  journal={Discrete Mathematics},
It was conjectured by Caccetta and H aggkvist in 1978 that the girth of every digraph with n vertices and minimum outdegree r is at most dn=re. The conjecture was proved for r = 2 by Caccetta and H aggkvist, for r = 3 by Hamidoune and for r = 4; 5 by Ho ang and Reed. In this paper, the following two main results are proved: 1. The diameter of every strongly connected digraph of order n with girth g is at most n−g+ t, where t is the number of vertices having outdegree exactly 1. As a… CONTINUE READING